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On Graded 2-Prime Ideals

Author

Listed:
  • Malik Bataineh

    (Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan)

  • Rashid Abu-Dawwas

    (Department of Mathematics, Yarmouk University, Irbid 22110, Jordan)

Abstract

The purpose of this paper is to introduce the concept of graded 2-prime ideals as a new generalization of graded prime ideals. We show that graded 2-prime ideals and graded semi-prime ideals are different. Furthermore, we show that graded 2-prime ideals and graded weakly prime ideals are also different. Several properties of graded 2-prime ideals are investigated. We study graded rings in which every graded 2-prime ideal is graded prime, we call such a graded ring a graded 2-P-ring. Moreover, we introduce the concept of graded semi-primary ideals, and show that graded 2-prime ideals and graded semi-primary ideals are different concepts. In fact, we show that graded semi-primary, graded 2-prime and graded primary ideals are equivalent over Z -graded principal ideal domain.

Suggested Citation

  • Malik Bataineh & Rashid Abu-Dawwas, 2021. "On Graded 2-Prime Ideals," Mathematics, MDPI, vol. 9(5), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:493-:d:507494
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    Cited by:

    1. Azzh Saad Alshehry & Rashid Abu-Dawwas & Basel Hawary, 2024. "Graded Weakly Strongly Quasi-Primary Ideals over Commutative Graded Rings," Mathematics, MDPI, vol. 12(18), pages 1-10, September.

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